This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##   [1] "re_dsr"         "beta1_pH"       "beta3_pH"       "re_pH"         
##   [5] "mu_beta1_pH"    "beta0_pH"       "p_dsr"          "re_pelagic"    
##   [9] "re_black"       "beta2_pH"       "pH"             "Ro_ay"         
##  [13] "Hd_ayg"         "Ro_ayg"         "Ry_ayg"         "Ry_ayg_mort"   
##  [17] "beta4_pH"       "pDSR_YE_ay"     "re_yellow"      "mu_beta0_pH"   
##  [21] "Ty_ayg"         "p_yellow"       "pDSR_YE_ayu"    "mu_beta2_pH"   
##  [25] "pDSR_YE_ayg"    "Rdnye_ayg"      "Rdnye_ayg_mort" "tau_beta1_pH"  
##  [29] "Rb_ay_mort"     "Rp_ay_mort"     "Ry_ayu"         "Ry_ayu_mort"   
##  [33] "Rp_ay"          "Rb_ay"          "Ry_ay"          "Ry_ay_mort"    
##  [37] "Ty_ayu"         "By_ayu"         "Ty_ay"          "By_ay"         
##  [41] "Rdnye_ay"       "Rdnye_ay_mort"  "Rp_ayg"         "Rp_ayg_mort"   
##  [45] "Rb_ayg_mort"    "Rb_ayg"         "mu_beta4_pH"    "By_ayg"        
##  [49] "Ro_ayu"         "Rs_ayg"         "Rs_ayg_mort"    "Hdnye_ayg"     
##  [53] "p_pelagic"      "Hy_ayg"         "R_ayg"          "Ts_ayg"        
##  [57] "Bs_ayg"         "tau_beta0_pH"   "Hp_ay"          "Rd_ayg"        
##  [61] "Rs_ay"          "Rs_ay_mort"     "Bs_ay"          "Rd_ay"         
##  [65] "Tdnye_ayg"      "Bb_ayg"         "Tp_ayg"         "Tb_ayg"        
##  [69] "R_ay"           "Rb_ayu"         "Rb_ayu_mort"    "Tb_ay"         
##  [73] "Rp_ayu"         "Rp_ayu_mort"    "Bp_ay"          "Bp_ayg"        
##  [77] "Bb_ay"          "Tp_ay"          "R_ayu"          "Bb_ayu"        
##  [81] "Tb_ayu"         "Tp_ayu"         "Bp_ayu"         "Bdnye_ay"      
##  [85] "Ts_ay"          "Tdnye_ay"       "Bdnye_ayg"      "Bs_ayu"        
##  [89] "Rd_ayu"         "Rdnye_ayu_mort" "Rdnye_ayu"      "Hb_ay"         
##  [93] "Rs_ayu"         "Rs_ayu_mort"    "Ts_ayu"         "re_slope"      
##  [97] "mu2_wt"         "mu_wt"          "Ho_ayg"         "p_black"       
## [101] "Hb_ayg"         "Hy_ay"          "Hy_ayu"         "Hd_ay"         
## [105] "tau_beta2_pH"   "tau_beta4_pH"   "Bdnye_ayu"      "mu3_wt"        
## [109] "Tdnye_ayu"      "Hp_ayg"         "Hp_ayu"         "Ho_ay"         
## [113] "Hdnye_ay"       "Htrend_ay"      "H_ayg"          "beta_H"        
## [117] "pG"             "Hb_ayu"         "Ho_ayu"         "H_ayu"         
## [121] "H_ay"           "Hd_ayu"         "Hs_ayu"         "Hdnye_ayu"     
## [125] "Hs_ay"          "sd_wt"          "logbc_H"        "Hs_ayg"        
## [129] "logRhat_ay"     "tau_beta3_pH"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_black 2 2.500796
sd_comp 1 1.959793
beta1_yellow 5 1.846165
beta0_yellow 5 1.776675
beta0_black 2 1.716180
beta1_pelagic 4 1.628713
beta3_pH 15 1.606165
beta0_pelagic 7 1.576434
beta1_pH 32 1.549286
beta0_pH 23 1.444278
mu_beta0_pH 3 1.387383
parameter n badRhat_avg
beta3_pelagic 4 1.372912
beta2_pH 20 1.335377
beta3_yellow 4 1.335060
beta3_black 2 1.317863
beta2_pelagic 6 1.313342
tau_beta0_pH 4 1.246439
mu_beta0_yellow 1 1.246013
tau_beta0_yellow 1 1.205614
beta2_yellow 5 1.176881
beta_H 1 1.161740
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta0_pH 2 1 0 1 0 1 1 1 0 0 3 2 3 2 3 3
beta0_pH 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1
beta1_pH 2 1 2 2 2 2 1 1 1 1 3 2 3 3 3 3
beta1_pH 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
beta2_pH 1 1 1 1 0 0 1 0 1 0 3 2 2 2 2 3
beta2_pH 1 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1
beta3_pH 0 1 0 1 1 0 0 0 0 0 3 1 3 1 1 3
beta3_pH 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1
beta4_pH 1 2 2 1 1 0 1 1 1 2 1 1 1 1 2 1
Bp_ay 0 0 0 0 0 0 0 0 0 0 3 11 13 11 10 14
Bp_ayg 0 0 0 0 0 0 0 0 0 0 6 12 12 10 11 15
Bp_ayu 0 0 0 0 0 0 0 0 0 0 12 12 12 11 11 11
H_ay 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 1
H_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8
H_ayu 0 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0
Hb_ay 0 0 13 0 0 0 0 1 0 0 2 0 8 1 0 0
Hb_ayg 0 0 7 0 0 0 0 1 0 0 0 0 8 0 0 0
Hb_ayu 0 0 7 0 0 0 0 0 0 0 0 0 1 1 0 0
Hd_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 1 24 4
Hd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28 4
Hd_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Hdnye_ay 0 0 0 0 0 0 0 0 0 0 1 0 1 2 14 8
Hdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 22 12
Hdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Ho_ay 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 10
Ho_ayg 0 0 0 0 0 0 1 1 0 0 0 0 0 0 5 13
Ho_ayu 0 0 0 0 1 0 0 0 3 0 0 0 1 0 0 0
Hp_ay 0 1 16 0 0 0 0 0 0 0 3 0 1 1 0 0
Hp_ayg 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0
Hp_ayu 0 1 9 0 0 0 0 0 0 0 0 0 1 1 0 1
Hs_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Hs_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Hs_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Htrend_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16
Hy_ay 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 3
Hy_ayg 0 0 1 0 0 0 0 0 0 0 0 1 3 1 0 0
Hy_ayu 0 0 0 0 0 0 0 1 6 0 1 0 1 0 0 2
logbc_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5
logRhat_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
mu_beta0_pH 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta1_pH 2 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta2_pH 1 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta4_pH 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p_black 0 0 0 0 0 0 0 1 0 0 0 0 58 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 0 5 0 0 61 0
p_pelagic 0 0 27 0 0 0 0 0 0 0 5 0 0 0 0 3
p_yellow 0 0 0 0 0 0 0 0 0 0 1 1 2 6 1 4
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 1 1 0 3 0 3
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 0 1 2 3 1 2
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 1 0 0 3 0 2
pG 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0
pH 53 142 69 3 33 5 10 6 26 70 74 20 56 14 101 144
R_ay 13 11 9 11 18 16 13 14 13 12 12 13 11 11 10 13
R_ayg 13 21 11 13 14 15 13 13 14 13 18 13 11 10 11 12
R_ayu 9 14 7 13 17 15 12 13 13 10 14 12 12 13 11 12
Rb_ay 12 21 14 12 22 18 14 13 16 17 20 14 22 12 16 29
Rb_ay_mort 12 22 12 12 21 18 14 13 16 17 20 14 22 12 16 29
Rb_ayg 12 21 11 13 16 14 12 12 15 13 12 13 19 11 12 21
Rb_ayg_mort 12 21 11 13 16 14 12 12 15 13 12 13 19 11 12 21
Rb_ayu 13 18 13 18 22 17 14 13 14 17 25 13 18 15 24 24
Rb_ayu_mort 13 18 13 18 22 17 14 13 14 17 25 13 18 15 24 24
Rd_ay 0 0 0 0 0 0 0 0 0 0 18 10 11 7 10 9
Rd_ayg 0 0 0 0 0 0 0 0 0 0 20 19 12 10 11 12
Rd_ayu 0 0 0 0 0 0 0 0 0 0 20 6 3 8 3 3
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 22
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 0 11 0 0 0 22
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 1 6 3 1 0 22
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 1 6 3 1 0 22
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 1 17 1 1 0 16
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 1 17 1 1 0 16
re_pelagic 0 18 5 0 0 0 0 0 0 0 31 0 12 12 20 38
re_pH 27 25 0 3 0 30 11 25 10 2 52 42 64 42 65 67
re_slope 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0
Ro_ay 1 20 10 1 18 10 6 2 4 5 3 10 8 0 9 32
Ro_ayg 10 3 1 2 4 3 5 2 2 1 1 7 21 1 7 29
Ro_ayu 1 20 8 1 18 10 4 2 3 5 3 13 4 0 6 19
Rp_ay 17 21 13 13 22 18 14 14 15 17 21 14 16 12 22 29
Rp_ay_mort 16 22 14 12 21 18 14 14 15 17 21 14 16 12 22 29
Rp_ayg 13 21 10 13 16 15 13 13 14 13 12 13 11 10 12 21
Rp_ayg_mort 13 21 10 13 16 15 13 13 14 13 12 13 11 10 12 21
Rp_ayu 14 18 14 18 20 17 14 14 14 16 27 13 18 14 24 24
Rp_ayu_mort 14 18 14 18 20 17 14 14 14 16 27 13 18 14 24 24
Rs_ay 0 0 0 0 0 0 0 0 0 0 0 7 0 0 1 21
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 0 7 0 0 1 21
Rs_ayg 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 22
Rs_ayg_mort 0 0 0 0 0 0 0 0 0 0 2 2 2 0 0 22
Rs_ayu 0 0 0 0 0 0 0 0 0 0 0 9 0 0 2 10
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 9 0 0 2 10
Ry_ay 15 39 37 11 33 22 17 12 19 6 29 16 20 12 25 20
Ry_ay_mort 15 39 37 11 33 22 17 12 19 6 29 16 20 12 25 20
Ry_ayg 16 10 17 10 18 22 18 20 25 26 21 20 26 12 28 28
Ry_ayg_mort 16 10 17 10 18 22 18 20 25 26 21 20 26 12 28 28
Ry_ayu 17 33 36 8 33 22 15 9 18 6 32 11 8 11 21 8
Ry_ayu_mort 17 33 36 8 33 22 15 9 18 6 32 11 8 11 21 8
tau_beta0_pH 1 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta1_pH 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta2_pH 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta3_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta4_pH 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Tp_ay 13 9 12 11 13 10 13 13 12 12 7 12 12 12 11 14
Tp_ayg 13 6 9 13 13 14 13 13 12 13 6 12 11 10 11 15
Tp_ayu 4 3 8 10 12 9 11 12 12 10 12 12 12 14 10 11
beta0_black 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta0_pelagic 0 1 1 0 0 0 0 0 0 0 1 0 1 1 1 1
beta0_yellow 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1
beta1_black 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta1_pelagic 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 1
beta1_yellow 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1
beta2_pelagic 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1
beta2_yellow 0 1 0 1 0 0 0 0 0 0 1 0 0 1 1 0
beta3_black 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta3_pelagic 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1
beta3_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1
mu_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.146 0.073 -0.285 -0.147 -0.002
mu_bc_H[2] -0.124 0.042 -0.200 -0.126 -0.038
mu_bc_H[3] -0.457 0.073 -0.590 -0.462 -0.305
mu_bc_H[4] -1.052 0.201 -1.468 -1.049 -0.663
mu_bc_H[5] 0.731 0.907 -0.345 0.573 2.647
mu_bc_H[6] -2.191 0.315 -2.776 -2.205 -1.542
mu_bc_H[7] -0.489 0.111 -0.709 -0.488 -0.280
mu_bc_H[8] 0.074 0.306 -0.423 0.040 0.802
mu_bc_H[9] -0.348 0.143 -0.642 -0.347 -0.067
mu_bc_H[10] -0.153 0.063 -0.276 -0.153 -0.023
mu_bc_H[11] -0.147 0.044 -0.234 -0.146 -0.063
mu_bc_H[12] -0.283 0.105 -0.517 -0.278 -0.091
mu_bc_H[13] -0.212 0.088 -0.375 -0.214 -0.043
mu_bc_H[14] -0.358 0.106 -0.581 -0.353 -0.165
mu_bc_H[15] -0.372 0.050 -0.468 -0.372 -0.273
mu_bc_H[16] -0.608 0.372 -1.288 -0.627 0.170
mu_bc_R[1] 1.458 0.150 1.165 1.457 1.747
mu_bc_R[2] 1.529 0.085 1.367 1.529 1.697
mu_bc_R[3] 1.458 0.149 1.166 1.456 1.753
mu_bc_R[4] 1.104 0.180 0.720 1.113 1.429
mu_bc_R[5] 1.652 0.495 0.694 1.651 2.588
mu_bc_R[6] -0.995 0.524 -2.025 -0.994 0.008
mu_bc_R[7] 0.448 0.155 0.134 0.455 0.744
mu_bc_R[8] 0.582 0.189 0.212 0.580 0.949
mu_bc_R[9] 0.527 0.169 0.176 0.534 0.836
mu_bc_R[10] 1.495 0.135 1.225 1.498 1.757
mu_bc_R[11] 1.097 0.123 0.870 1.089 1.354
mu_bc_R[12] 0.938 0.203 0.545 0.935 1.341
mu_bc_R[13] 1.112 0.107 0.909 1.110 1.332
mu_bc_R[14] 0.956 0.143 0.678 0.954 1.235
mu_bc_R[15] 0.881 0.120 0.651 0.879 1.127
mu_bc_R[16] 1.152 0.132 0.905 1.147 1.424
tau_pH[1] 0.246 0.394 0.040 0.086 1.660
tau_pH[2] 1.188 0.744 0.234 1.128 2.366
tau_pH[3] 2.163 0.543 0.929 2.107 3.256
beta0_pH[1,1] 3.933 1.514 1.155 4.012 6.335
beta0_pH[2,1] 7.297 3.001 1.067 7.915 12.222
beta0_pH[3,1] 5.022 2.116 1.602 5.051 9.535
beta0_pH[4,1] 4.488 1.926 1.984 3.951 9.604
beta0_pH[5,1] 2.178 1.139 0.090 2.096 4.403
beta0_pH[6,1] 1.460 0.802 0.044 1.384 2.948
beta0_pH[7,1] 2.910 1.335 0.514 3.123 5.235
beta0_pH[8,1] 2.861 1.697 -0.077 2.800 6.417
beta0_pH[9,1] 2.172 0.970 0.325 2.122 3.756
beta0_pH[10,1] 4.746 2.101 1.015 4.944 8.118
beta0_pH[11,1] 7.724 2.725 2.286 8.058 12.140
beta0_pH[12,1] 3.166 1.229 0.869 3.093 6.014
beta0_pH[13,1] 4.783 1.992 1.279 4.882 8.181
beta0_pH[14,1] 3.417 1.930 0.073 3.280 7.380
beta0_pH[15,1] 5.917 2.443 1.293 5.993 9.276
beta0_pH[16,1] 5.379 2.903 0.412 4.707 11.738
beta0_pH[1,2] 2.894 0.252 2.434 2.875 3.471
beta0_pH[2,2] 2.880 0.210 2.440 2.879 3.301
beta0_pH[3,2] 3.156 0.240 2.744 3.133 3.732
beta0_pH[4,2] 3.035 0.244 2.662 2.992 3.674
beta0_pH[5,2] 4.771 1.523 2.852 4.440 8.723
beta0_pH[6,2] 3.205 0.340 2.635 3.168 4.013
beta0_pH[7,2] 1.817 0.307 1.220 1.813 2.472
beta0_pH[8,2] 2.888 0.289 2.308 2.886 3.512
beta0_pH[9,2] 3.541 0.380 2.859 3.503 4.399
beta0_pH[10,2] 3.656 0.312 3.050 3.643 4.340
beta0_pH[11,2] -1.915 2.840 -5.275 -1.942 3.624
beta0_pH[12,2] -3.249 2.231 -5.496 -4.343 0.900
beta0_pH[13,2] -2.516 2.295 -5.142 -3.725 1.204
beta0_pH[14,2] -3.719 2.808 -6.811 -5.199 1.043
beta0_pH[15,2] -2.408 2.257 -4.838 -3.718 1.351
beta0_pH[16,2] -3.051 2.477 -5.515 -4.384 1.469
beta0_pH[1,3] -0.365 0.759 -2.199 -0.282 0.888
beta0_pH[2,3] 2.180 0.170 1.843 2.185 2.502
beta0_pH[3,3] 2.520 0.155 2.222 2.518 2.824
beta0_pH[4,3] 2.962 0.168 2.638 2.963 3.299
beta0_pH[5,3] 1.141 0.691 0.222 1.019 2.850
beta0_pH[6,3] 0.718 0.550 -0.488 0.778 1.684
beta0_pH[7,3] 0.714 0.192 0.337 0.719 1.070
beta0_pH[8,3] 0.320 0.202 -0.085 0.313 0.724
beta0_pH[9,3] -0.437 0.434 -1.304 -0.434 0.411
beta0_pH[10,3] 0.508 0.409 -0.610 0.557 1.123
beta0_pH[11,3] -0.127 0.655 -1.195 -0.184 1.735
beta0_pH[12,3] -0.917 0.501 -1.831 -0.921 -0.055
beta0_pH[13,3] 0.040 0.577 -0.931 -0.053 1.456
beta0_pH[14,3] -0.187 0.418 -0.810 -0.248 1.058
beta0_pH[15,3] -0.400 1.280 -2.011 -0.750 3.538
beta0_pH[16,3] -0.269 0.581 -1.427 -0.303 1.075
beta1_pH[1,1] 0.341 0.600 0.000 0.017 2.045
beta1_pH[2,1] 0.926 1.214 0.000 0.060 3.067
beta1_pH[3,1] 0.288 0.604 0.000 0.018 1.770
beta1_pH[4,1] 0.898 1.206 0.000 0.126 3.532
beta1_pH[5,1] 0.127 0.401 0.000 0.000 1.578
beta1_pH[6,1] 0.123 0.373 0.000 0.000 1.494
beta1_pH[7,1] 0.079 0.260 0.000 0.000 1.070
beta1_pH[8,1] 0.184 0.541 0.000 0.000 2.061
beta1_pH[9,1] 0.073 0.250 0.000 0.000 0.880
beta1_pH[10,1] 0.077 0.268 0.000 0.000 1.102
beta1_pH[11,1] 0.784 0.995 0.000 0.096 2.900
beta1_pH[12,1] 0.358 0.618 0.000 0.015 2.186
beta1_pH[13,1] 0.721 0.946 0.000 0.105 3.471
beta1_pH[14,1] 0.604 0.878 0.000 0.045 2.764
beta1_pH[15,1] 0.269 0.424 0.000 0.024 1.454
beta1_pH[16,1] 0.533 0.857 0.000 0.019 2.980
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.002 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.001 0.000 0.000 0.000
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 3.590 2.796 0.000 3.760 6.983
beta1_pH[12,2] 4.627 2.600 0.000 5.914 7.191
beta1_pH[13,2] 4.279 2.924 0.000 5.916 7.506
beta1_pH[14,2] 5.061 3.143 0.000 6.779 8.372
beta1_pH[15,2] 4.360 2.889 0.000 6.111 7.376
beta1_pH[16,2] 5.163 3.130 0.000 6.901 8.171
beta1_pH[1,3] 4.960 1.659 2.425 4.704 8.474
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 5.290 5.526 1.164 2.869 17.140
beta1_pH[6,3] 2.871 3.825 0.291 2.144 12.083
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.691 0.385 1.959 2.686 3.459
beta1_pH[9,3] 2.562 0.501 1.633 2.557 3.568
beta1_pH[10,3] 2.815 0.522 1.967 2.759 4.135
beta1_pH[11,3] 2.560 0.858 0.018 2.697 3.832
beta1_pH[12,3] 4.151 0.597 2.995 4.168 5.297
beta1_pH[13,3] 1.570 0.651 0.004 1.644 2.604
beta1_pH[14,3] 2.429 0.528 0.962 2.509 3.203
beta1_pH[15,3] 1.833 0.869 0.001 2.059 3.159
beta1_pH[16,3] 1.671 0.685 0.005 1.768 2.896
beta2_pH[1,1] 2.282 6.908 -8.985 2.185 19.063
beta2_pH[2,1] 2.364 6.888 -10.554 2.412 18.523
beta2_pH[3,1] 2.303 7.152 -10.699 2.084 19.422
beta2_pH[4,1] 2.292 7.060 -9.998 1.781 18.289
beta2_pH[5,1] 0.317 3.033 -5.927 0.213 6.946
beta2_pH[6,1] 0.607 2.886 -5.052 0.413 6.584
beta2_pH[7,1] 0.314 2.237 0.000 0.000 2.278
beta2_pH[8,1] 0.372 2.945 -5.768 0.358 6.579
beta2_pH[9,1] 1.580 2.784 -3.264 0.740 6.984
beta2_pH[10,1] -0.285 3.066 -6.001 -0.062 6.328
beta2_pH[11,1] 1.476 6.688 -15.583 1.939 14.107
beta2_pH[12,1] 0.947 6.362 -16.167 1.478 13.497
beta2_pH[13,1] 1.537 6.844 -16.418 2.092 13.886
beta2_pH[14,1] 1.583 6.786 -16.022 2.213 14.265
beta2_pH[15,1] 0.619 6.892 -16.009 0.932 14.186
beta2_pH[16,1] 1.492 6.799 -16.519 2.233 13.908
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -1.985 1.807 -6.839 -1.545 -0.032
beta2_pH[4,2] -1.993 1.796 -6.610 -1.572 -0.034
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -8.930 6.901 -24.094 -8.212 6.673
beta2_pH[12,2] -8.235 7.111 -24.218 -7.433 6.894
beta2_pH[13,2] -8.168 7.186 -24.417 -7.210 7.144
beta2_pH[14,2] -8.330 7.060 -23.787 -7.467 6.882
beta2_pH[15,2] -8.925 6.993 -24.820 -8.126 6.681
beta2_pH[16,2] -9.106 6.842 -23.875 -8.457 6.314
beta2_pH[1,3] 0.188 0.112 0.100 0.155 0.444
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 9.361 6.092 0.624 8.432 23.649
beta2_pH[6,3] 9.318 6.131 0.209 8.526 23.194
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.078 5.656 1.778 9.060 23.235
beta2_pH[9,3] 9.332 6.102 0.613 8.326 23.121
beta2_pH[10,3] 8.707 6.398 0.452 7.751 23.187
beta2_pH[11,3] -2.312 2.314 -8.447 -1.636 -0.474
beta2_pH[12,3] -2.291 1.772 -7.792 -1.743 -0.821
beta2_pH[13,3] -2.746 2.469 -9.330 -2.057 0.947
beta2_pH[14,3] -2.883 2.304 -9.381 -2.093 -0.778
beta2_pH[15,3] -2.756 2.263 -9.128 -2.141 -0.116
beta2_pH[16,3] -1.377 2.640 -7.987 -1.513 3.205
beta3_pH[1,1] 31.304 7.932 18.677 32.042 44.776
beta3_pH[2,1] 28.054 7.677 18.548 24.731 44.947
beta3_pH[3,1] 29.917 7.478 18.475 30.136 44.461
beta3_pH[4,1] 27.504 7.562 18.288 25.286 44.458
beta3_pH[5,1] 30.259 7.779 18.663 29.426 44.655
beta3_pH[6,1] 30.439 7.844 18.571 30.192 44.939
beta3_pH[7,1] 30.095 8.046 18.471 29.175 45.098
beta3_pH[8,1] 30.338 8.182 18.439 29.397 44.876
beta3_pH[9,1] 29.996 7.640 18.432 29.768 44.822
beta3_pH[10,1] 29.094 7.308 18.429 28.980 44.014
beta3_pH[11,1] 35.951 4.906 29.195 34.368 45.365
beta3_pH[12,1] 37.054 5.322 29.315 36.888 45.642
beta3_pH[13,1] 38.764 5.059 30.459 39.671 45.820
beta3_pH[14,1] 36.493 4.936 29.515 35.823 45.482
beta3_pH[15,1] 37.417 4.846 29.474 36.949 45.514
beta3_pH[16,1] 36.260 5.900 29.319 34.622 45.359
beta3_pH[1,2] 29.831 7.917 18.423 28.982 44.830
beta3_pH[2,2] 29.970 7.909 18.465 28.929 45.018
beta3_pH[3,2] 29.724 7.964 18.424 28.636 44.545
beta3_pH[4,2] 30.016 8.001 18.481 29.182 44.899
beta3_pH[5,2] 29.897 7.786 18.438 29.064 44.876
beta3_pH[6,2] 29.945 8.010 18.399 28.951 45.020
beta3_pH[7,2] 29.869 7.978 18.476 28.581 44.542
beta3_pH[8,2] 29.917 7.861 18.466 28.891 44.831
beta3_pH[9,2] 30.190 8.031 18.519 29.367 44.862
beta3_pH[10,2] 30.030 8.029 18.523 28.983 45.088
beta3_pH[11,2] 40.281 4.134 30.016 43.058 43.882
beta3_pH[12,2] 41.765 3.511 30.376 43.122 44.104
beta3_pH[13,2] 42.180 3.671 30.629 43.750 44.669
beta3_pH[14,2] 41.803 3.552 30.490 43.238 44.240
beta3_pH[15,2] 41.817 3.600 30.361 43.293 43.906
beta3_pH[16,2] 41.967 3.499 30.662 43.414 43.993
beta3_pH[1,3] 38.577 3.632 31.519 38.410 45.314
beta3_pH[2,3] 30.091 7.969 18.388 29.418 44.697
beta3_pH[3,3] 30.283 8.083 18.543 29.558 44.833
beta3_pH[4,3] 30.520 8.006 18.506 29.735 45.021
beta3_pH[5,3] 40.680 3.773 32.057 41.873 45.350
beta3_pH[6,3] 38.261 4.680 31.245 39.144 45.507
beta3_pH[7,3] 37.934 4.280 31.314 37.593 45.530
beta3_pH[8,3] 41.485 0.288 41.023 41.482 41.948
beta3_pH[9,3] 33.595 0.551 32.120 33.645 34.665
beta3_pH[10,3] 35.858 0.797 33.420 36.031 36.859
beta3_pH[11,3] 41.916 1.682 37.229 42.231 43.546
beta3_pH[12,3] 41.797 0.482 40.909 41.813 42.697
beta3_pH[13,3] 42.024 2.524 32.308 42.503 44.731
beta3_pH[14,3] 41.017 1.045 39.324 41.124 42.153
beta3_pH[15,3] 42.305 1.798 36.931 42.667 44.436
beta3_pH[16,3] 38.982 5.902 29.087 42.537 44.153
beta0_pelagic[1] 2.208 0.126 1.968 2.207 2.464
beta0_pelagic[2] 1.464 0.116 1.244 1.458 1.681
beta0_pelagic[3] -0.330 0.612 -1.537 -0.171 0.509
beta0_pelagic[4] 0.310 0.277 -0.216 0.317 0.819
beta0_pelagic[5] 1.149 0.256 0.626 1.157 1.635
beta0_pelagic[6] 1.448 0.287 0.815 1.474 1.950
beta0_pelagic[7] 1.629 0.223 1.221 1.618 2.099
beta0_pelagic[8] 1.729 0.198 1.328 1.732 2.131
beta0_pelagic[9] 2.486 0.318 1.892 2.496 3.085
beta0_pelagic[10] 2.499 0.198 2.069 2.503 2.874
beta0_pelagic[11] -0.264 0.384 -0.865 -0.314 0.403
beta0_pelagic[12] 1.663 0.157 1.365 1.663 1.971
beta0_pelagic[13] 0.214 0.194 -0.217 0.243 0.540
beta0_pelagic[14] -0.111 0.224 -0.572 -0.099 0.296
beta0_pelagic[15] -0.348 0.143 -0.642 -0.341 -0.076
beta0_pelagic[16] 0.067 0.256 -0.443 0.054 0.539
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.645 0.773 0.517 1.488 3.172
beta1_pelagic[4] 0.929 0.309 0.362 0.912 1.538
beta1_pelagic[5] -0.075 0.308 -0.667 -0.071 0.550
beta1_pelagic[6] -0.176 0.502 -0.966 -0.278 0.797
beta1_pelagic[7] -0.010 0.304 -0.587 -0.016 0.591
beta1_pelagic[8] -0.016 0.270 -0.525 -0.026 0.539
beta1_pelagic[9] 0.179 0.505 -0.787 0.291 0.939
beta1_pelagic[10] 0.035 0.275 -0.499 0.038 0.603
beta1_pelagic[11] 3.098 0.528 2.213 3.084 3.981
beta1_pelagic[12] 2.869 0.303 2.262 2.868 3.461
beta1_pelagic[13] 3.108 0.598 2.140 3.052 4.432
beta1_pelagic[14] 3.849 0.571 2.956 3.791 5.192
beta1_pelagic[15] 2.991 0.241 2.517 2.989 3.451
beta1_pelagic[16] 3.795 0.655 2.724 3.711 5.095
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.773 2.412 0.045 0.195 7.137
beta2_pelagic[4] 2.268 4.042 0.056 0.640 15.523
beta2_pelagic[5] -0.022 0.691 -1.426 -0.020 1.435
beta2_pelagic[6] -0.196 0.715 -1.551 -0.259 1.236
beta2_pelagic[7] -0.009 0.677 -1.484 -0.008 1.367
beta2_pelagic[8] 0.145 0.658 -1.193 0.108 1.408
beta2_pelagic[9] 0.135 0.692 -1.308 0.231 1.385
beta2_pelagic[10] 0.022 0.707 -1.422 0.017 1.666
beta2_pelagic[11] 0.302 0.177 0.134 0.237 0.778
beta2_pelagic[12] 4.251 3.413 0.984 3.211 13.957
beta2_pelagic[13] 0.476 0.273 0.178 0.402 1.201
beta2_pelagic[14] 0.317 0.089 0.194 0.297 0.539
beta2_pelagic[15] 4.610 3.734 0.857 3.627 16.014
beta2_pelagic[16] 1.359 2.444 0.223 0.419 8.873
beta3_pelagic[1] 29.881 7.899 18.454 28.710 45.057
beta3_pelagic[2] 29.750 7.818 18.469 28.679 44.723
beta3_pelagic[3] 28.468 5.813 19.540 27.635 43.465
beta3_pelagic[4] 26.425 3.663 20.411 25.994 35.961
beta3_pelagic[5] 30.194 8.223 18.530 28.910 45.207
beta3_pelagic[6] 31.837 6.185 19.557 31.497 43.795
beta3_pelagic[7] 29.649 7.583 18.402 28.644 44.717
beta3_pelagic[8] 29.583 8.210 18.417 27.963 45.136
beta3_pelagic[9] 31.096 6.084 19.230 31.195 43.594
beta3_pelagic[10] 29.619 8.080 18.336 28.371 44.683
beta3_pelagic[11] 37.711 2.880 32.450 37.477 42.698
beta3_pelagic[12] 43.466 0.287 42.975 43.442 44.096
beta3_pelagic[13] 42.740 1.365 39.981 42.685 45.718
beta3_pelagic[14] 41.184 1.618 37.819 41.231 44.545
beta3_pelagic[15] 43.137 0.256 42.628 43.149 43.639
beta3_pelagic[16] 42.204 1.195 39.308 42.478 43.735
mu_beta0_pelagic[1] 0.834 0.968 -1.302 0.908 2.649
mu_beta0_pelagic[2] 1.796 0.385 0.956 1.801 2.543
mu_beta0_pelagic[3] 0.211 0.491 -0.768 0.214 1.186
tau_beta0_pelagic[1] 0.623 0.665 0.053 0.408 2.464
tau_beta0_pelagic[2] 2.648 3.272 0.265 1.893 8.905
tau_beta0_pelagic[3] 1.385 1.028 0.160 1.152 3.953
beta0_yellow[1] -0.542 0.198 -1.009 -0.521 -0.215
beta0_yellow[2] 0.521 0.159 0.193 0.529 0.812
beta0_yellow[3] -0.317 0.174 -0.645 -0.319 0.018
beta0_yellow[4] 0.849 0.244 0.272 0.884 1.202
beta0_yellow[5] -0.357 0.351 -1.041 -0.358 0.345
beta0_yellow[6] 1.112 0.165 0.795 1.110 1.441
beta0_yellow[7] 1.031 0.161 0.718 1.030 1.354
beta0_yellow[8] 0.998 0.158 0.685 1.001 1.309
beta0_yellow[9] 0.661 0.162 0.343 0.658 0.976
beta0_yellow[10] 0.589 0.143 0.306 0.587 0.868
beta0_yellow[11] -1.558 0.532 -2.676 -1.619 -0.520
beta0_yellow[12] -3.543 0.478 -4.546 -3.521 -2.599
beta0_yellow[13] -3.709 0.449 -4.488 -3.739 -2.831
beta0_yellow[14] -1.755 0.783 -3.032 -1.870 -0.124
beta0_yellow[15] -2.565 0.495 -3.619 -2.574 -1.584
beta0_yellow[16] -1.877 0.655 -2.887 -1.951 -0.375
beta1_yellow[1] 0.630 0.501 0.007 0.561 1.812
beta1_yellow[2] 0.992 0.336 0.520 0.953 1.718
beta1_yellow[3] 0.678 0.229 0.205 0.681 1.109
beta1_yellow[4] 1.319 0.592 0.623 1.180 3.036
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 1.749 0.562 0.649 1.814 3.042
beta1_yellow[12] 2.348 0.499 1.357 2.330 3.366
beta1_yellow[13] 2.907 0.442 2.050 2.939 3.651
beta1_yellow[14] 1.824 0.777 0.134 1.938 3.082
beta1_yellow[15] 1.884 0.521 0.906 1.896 2.995
beta1_yellow[16] 1.675 0.699 0.067 1.784 2.776
beta2_yellow[1] -2.971 2.725 -9.834 -2.181 -0.024
beta2_yellow[2] -2.663 2.360 -8.888 -1.916 -0.196
beta2_yellow[3] -2.810 2.483 -9.068 -2.051 -0.191
beta2_yellow[4] -2.193 2.220 -7.340 -1.297 -0.112
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.646 2.649 -11.448 -3.999 -1.366
beta2_yellow[12] -4.834 2.621 -11.531 -4.257 -1.397
beta2_yellow[13] -4.659 2.579 -11.402 -4.038 -1.558
beta2_yellow[14] -4.426 2.407 -10.620 -4.040 -1.156
beta2_yellow[15] -4.448 2.674 -11.479 -3.844 -1.077
beta2_yellow[16] -5.004 2.653 -11.763 -4.452 -1.412
beta3_yellow[1] 27.132 7.525 18.321 24.121 44.660
beta3_yellow[2] 29.428 2.210 25.019 29.164 34.157
beta3_yellow[3] 33.024 2.940 26.956 32.873 39.383
beta3_yellow[4] 29.350 3.520 22.980 28.337 36.139
beta3_yellow[5] 30.022 7.992 18.541 29.011 44.880
beta3_yellow[6] 30.006 7.960 18.494 29.091 44.877
beta3_yellow[7] 30.070 7.903 18.520 29.233 44.746
beta3_yellow[8] 30.071 7.883 18.404 29.333 44.871
beta3_yellow[9] 30.181 8.057 18.390 29.319 44.883
beta3_yellow[10] 30.121 7.931 18.484 29.296 44.955
beta3_yellow[11] 45.083 0.632 43.553 45.188 45.941
beta3_yellow[12] 43.277 0.478 42.382 43.267 44.095
beta3_yellow[13] 44.910 0.393 44.014 44.979 45.556
beta3_yellow[14] 43.340 2.768 34.248 44.070 45.771
beta3_yellow[15] 45.012 0.569 43.925 44.995 45.951
beta3_yellow[16] 44.249 1.429 39.706 44.412 45.804
mu_beta0_yellow[1] 0.118 0.549 -1.126 0.123 1.203
mu_beta0_yellow[2] 0.644 0.356 -0.142 0.659 1.317
mu_beta0_yellow[3] -2.129 0.765 -3.321 -2.257 -0.382
tau_beta0_yellow[1] 1.780 1.987 0.091 1.160 7.307
tau_beta0_yellow[2] 3.097 3.866 0.279 2.079 11.728
tau_beta0_yellow[3] 1.078 1.184 0.081 0.672 4.447
beta0_black[1] -0.027 0.173 -0.357 -0.028 0.321
beta0_black[2] 1.914 0.131 1.662 1.914 2.176
beta0_black[3] 1.315 0.132 1.050 1.313 1.581
beta0_black[4] 2.426 0.133 2.169 2.426 2.682
beta0_black[5] 4.611 2.002 1.850 4.223 9.904
beta0_black[6] 4.625 2.015 2.260 4.102 9.864
beta0_black[7] 3.765 1.939 1.550 3.267 8.929
beta0_black[8] 0.947 0.210 0.542 0.946 1.356
beta0_black[9] 2.611 0.235 2.160 2.611 3.091
beta0_black[10] 1.460 0.136 1.202 1.459 1.729
beta0_black[11] 3.477 0.153 3.169 3.477 3.770
beta0_black[12] 4.862 0.175 4.513 4.862 5.208
beta0_black[13] 0.258 0.405 -0.424 0.219 1.045
beta0_black[14] 2.853 0.156 2.551 2.852 3.167
beta0_black[15] 1.302 0.156 0.996 1.301 1.598
beta0_black[16] 4.275 0.161 3.945 4.276 4.585
beta2_black[1] 7.772 9.929 0.280 3.454 38.512
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.339 1.845 -7.383 -1.813 -0.259
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.329 1.958 36.666 41.708 43.379
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 38.283 3.704 23.087 39.193 41.117
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.265 0.193 -0.640 -0.260 0.100
beta4_black[2] 0.250 0.187 -0.113 0.249 0.614
beta4_black[3] -0.935 0.193 -1.313 -0.934 -0.554
beta4_black[4] 0.434 0.220 -0.014 0.434 0.866
beta4_black[5] 0.565 1.371 -1.315 0.323 3.826
beta4_black[6] 0.537 1.312 -1.278 0.321 3.621
beta4_black[7] 0.450 1.259 -1.393 0.249 3.500
beta4_black[8] -0.226 0.317 -0.843 -0.220 0.381
beta4_black[9] 0.825 0.774 -0.248 0.666 2.786
beta4_black[10] 0.049 0.188 -0.316 0.050 0.418
beta4_black[11] -0.683 0.215 -1.100 -0.685 -0.252
beta4_black[12] 0.164 0.323 -0.444 0.154 0.829
beta4_black[13] -1.188 0.220 -1.633 -1.181 -0.776
beta4_black[14] -0.175 0.238 -0.628 -0.182 0.299
beta4_black[15] -0.894 0.221 -1.319 -0.888 -0.470
beta4_black[16] -0.601 0.235 -1.057 -0.604 -0.138
mu_beta0_black[1] 1.298 0.897 -0.611 1.309 3.012
mu_beta0_black[2] 2.712 1.070 0.658 2.598 5.129
mu_beta0_black[3] 2.602 0.969 0.440 2.672 4.427
tau_beta0_black[1] 0.652 0.628 0.057 0.451 2.398
tau_beta0_black[2] 0.437 0.585 0.046 0.243 2.000
tau_beta0_black[3] 0.269 0.192 0.053 0.223 0.772
beta0_dsr[11] -2.884 0.284 -3.422 -2.884 -2.312
beta0_dsr[12] 4.521 0.408 3.970 4.530 5.104
beta0_dsr[13] -1.337 0.292 -1.969 -1.331 -0.789
beta0_dsr[14] -3.765 0.589 -4.989 -3.749 -2.648
beta0_dsr[15] -2.354 0.836 -4.448 -2.068 -1.420
beta0_dsr[16] -3.011 0.369 -3.740 -3.003 -2.285
beta1_dsr[11] 4.864 0.298 4.274 4.866 5.415
beta1_dsr[12] 7.636 11.202 2.244 5.340 25.259
beta1_dsr[13] 2.868 0.300 2.309 2.857 3.489
beta1_dsr[14] 6.444 0.617 5.239 6.429 7.702
beta1_dsr[15] 5.664 3.486 2.880 3.551 13.454
beta1_dsr[16] 5.825 0.389 5.071 5.819 6.595
beta2_dsr[11] -6.872 2.795 -13.100 -6.525 -3.039
beta2_dsr[12] -6.264 2.853 -12.273 -6.123 -1.427
beta2_dsr[13] -5.559 2.814 -12.071 -5.315 -0.962
beta2_dsr[14] -5.303 2.717 -11.329 -4.845 -1.623
beta2_dsr[15] -5.141 4.119 -12.998 -5.989 -0.055
beta2_dsr[16] -7.379 2.445 -13.018 -7.061 -3.685
beta3_dsr[11] 43.491 0.145 43.220 43.488 43.780
beta3_dsr[12] 33.949 1.155 31.951 34.050 34.866
beta3_dsr[13] 43.232 0.347 42.587 43.206 43.850
beta3_dsr[14] 43.375 0.228 43.075 43.324 43.925
beta3_dsr[15] 39.362 5.934 28.993 43.375 43.837
beta3_dsr[16] 43.447 0.155 43.175 43.439 43.755
beta4_dsr[11] 0.558 0.220 0.137 0.554 1.007
beta4_dsr[12] 0.244 0.448 -0.639 0.243 1.151
beta4_dsr[13] -0.171 0.220 -0.603 -0.173 0.258
beta4_dsr[14] 0.156 0.254 -0.345 0.157 0.655
beta4_dsr[15] 0.728 0.217 0.313 0.725 1.159
beta4_dsr[16] 0.155 0.226 -0.295 0.153 0.593
beta0_slope[11] -1.926 0.176 -2.268 -1.926 -1.580
beta0_slope[12] -4.690 0.266 -5.236 -4.685 -4.186
beta0_slope[13] -1.394 0.274 -2.078 -1.355 -0.966
beta0_slope[14] -2.628 0.189 -3.001 -2.630 -2.263
beta0_slope[15] -1.413 0.327 -2.535 -1.374 -1.033
beta0_slope[16] -2.725 0.181 -3.077 -2.723 -2.378
beta1_slope[11] 4.592 0.314 3.959 4.599 5.217
beta1_slope[12] 5.024 0.537 4.017 5.013 6.119
beta1_slope[13] 3.151 0.721 2.278 2.965 5.187
beta1_slope[14] 6.533 0.590 5.404 6.520 7.763
beta1_slope[15] 3.156 0.529 2.487 3.072 5.078
beta1_slope[16] 5.390 0.406 4.627 5.384 6.222
beta2_slope[11] 7.963 2.330 4.353 7.602 13.396
beta2_slope[12] 6.951 2.602 2.248 6.747 12.772
beta2_slope[13] 4.877 3.304 0.274 5.070 11.475
beta2_slope[14] 6.335 2.487 2.307 6.126 12.152
beta2_slope[15] 7.105 2.830 0.226 7.038 12.901
beta2_slope[16] 7.512 2.371 3.793 7.139 13.145
beta3_slope[11] 43.480 0.155 43.196 43.479 43.777
beta3_slope[12] 43.414 0.234 43.061 43.391 43.890
beta3_slope[13] 43.643 0.612 42.245 43.741 44.912
beta3_slope[14] 43.333 0.180 43.094 43.292 43.772
beta3_slope[15] 43.469 0.610 42.860 43.511 43.945
beta3_slope[16] 43.455 0.167 43.174 43.444 43.798
beta4_slope[11] -0.589 0.225 -1.036 -0.589 -0.161
beta4_slope[12] -1.352 0.648 -2.796 -1.268 -0.322
beta4_slope[13] 0.031 0.229 -0.419 0.034 0.476
beta4_slope[14] -0.198 0.264 -0.718 -0.205 0.343
beta4_slope[15] -0.729 0.225 -1.190 -0.724 -0.291
beta4_slope[16] -0.211 0.241 -0.675 -0.218 0.262
sigma_H[1] 0.202 0.053 0.103 0.199 0.315
sigma_H[2] 0.170 0.030 0.118 0.167 0.235
sigma_H[3] 0.196 0.041 0.124 0.193 0.282
sigma_H[4] 0.393 0.074 0.271 0.388 0.558
sigma_H[5] 0.991 0.232 0.551 0.987 1.478
sigma_H[6] 0.302 0.184 0.016 0.291 0.696
sigma_H[7] 0.288 0.055 0.201 0.281 0.412
sigma_H[8] 0.457 0.138 0.301 0.430 0.792
sigma_H[9] 0.430 0.096 0.285 0.415 0.651
sigma_H[10] 0.225 0.045 0.152 0.221 0.324
sigma_H[11] 0.278 0.046 0.201 0.273 0.379
sigma_H[12] 0.452 0.172 0.207 0.434 0.782
sigma_H[13] 0.201 0.037 0.134 0.199 0.283
sigma_H[14] 0.458 0.087 0.314 0.449 0.648
sigma_H[15] 0.247 0.041 0.180 0.243 0.341
sigma_H[16] 0.244 0.047 0.167 0.239 0.356
lambda_H[1] 3.047 4.370 0.136 1.677 14.324
lambda_H[2] 9.247 8.417 0.909 6.691 32.256
lambda_H[3] 6.696 9.719 0.256 3.487 33.630
lambda_H[4] 0.007 0.005 0.001 0.006 0.019
lambda_H[5] 2.310 6.763 0.013 0.323 20.371
lambda_H[6] 6.839 13.048 0.009 1.678 34.754
lambda_H[7] 0.014 0.010 0.002 0.012 0.041
lambda_H[8] 3.742 7.726 0.000 0.161 25.537
lambda_H[9] 0.019 0.013 0.003 0.016 0.053
lambda_H[10] 0.322 0.635 0.031 0.192 1.255
lambda_H[11] 0.380 0.711 0.015 0.189 1.701
lambda_H[12] 5.781 7.264 0.269 3.522 25.200
lambda_H[13] 4.235 3.710 0.331 3.184 14.202
lambda_H[14] 3.326 3.682 0.276 2.255 12.213
lambda_H[15] 0.031 0.086 0.004 0.019 0.120
lambda_H[16] 2.953 3.852 0.124 1.678 13.648
mu_lambda_H[1] 4.431 1.949 1.280 4.254 8.580
mu_lambda_H[2] 3.461 1.900 0.275 3.362 7.311
mu_lambda_H[3] 3.766 1.805 1.016 3.521 7.977
sigma_lambda_H[1] 8.826 4.387 2.159 8.132 18.309
sigma_lambda_H[2] 8.025 4.822 0.455 7.603 18.075
sigma_lambda_H[3] 6.383 3.721 1.313 5.582 15.587
beta_H[1,1] 6.852 1.120 4.218 7.027 8.574
beta_H[2,1] 9.882 0.467 8.911 9.895 10.745
beta_H[3,1] 7.995 0.768 6.132 8.103 9.213
beta_H[4,1] 10.730 7.613 -4.089 10.728 26.144
beta_H[5,1] -0.040 3.200 -6.724 0.165 6.256
beta_H[6,1] 3.432 3.716 -6.177 4.724 7.544
beta_H[7,1] 1.509 5.475 -10.396 1.907 10.996
beta_H[8,1] 21.687 24.170 -2.483 2.892 65.061
beta_H[9,1] 13.764 5.457 3.724 13.500 24.863
beta_H[10,1] 7.162 1.737 3.592 7.207 10.679
beta_H[11,1] 5.927 3.189 -1.710 6.756 10.043
beta_H[12,1] 2.569 0.970 0.873 2.526 4.585
beta_H[13,1] 9.037 0.827 7.201 9.102 10.403
beta_H[14,1] 2.150 0.991 0.158 2.146 4.127
beta_H[15,1] -5.389 3.952 -12.522 -5.638 3.026
beta_H[16,1] 3.526 1.797 -0.111 3.568 6.934
beta_H[1,2] 7.911 0.256 7.378 7.913 8.393
beta_H[2,2] 10.042 0.131 9.780 10.043 10.290
beta_H[3,2] 8.974 0.191 8.598 8.973 9.366
beta_H[4,2] 3.087 1.471 0.274 3.035 6.080
beta_H[5,2] 1.914 1.073 -0.226 1.919 3.956
beta_H[6,2] 5.795 1.038 3.247 5.989 7.319
beta_H[7,2] 2.361 1.031 0.544 2.285 4.520
beta_H[8,2] -1.847 5.544 -11.105 1.717 4.174
beta_H[9,2] 2.924 1.031 0.880 2.928 5.003
beta_H[10,2] 8.153 0.359 7.398 8.167 8.804
beta_H[11,2] 9.625 0.579 8.788 9.505 11.017
beta_H[12,2] 3.978 0.359 3.308 3.975 4.707
beta_H[13,2] 9.173 0.231 8.733 9.169 9.630
beta_H[14,2] 4.061 0.340 3.402 4.059 4.744
beta_H[15,2] 11.252 0.712 9.770 11.286 12.504
beta_H[16,2] 5.302 0.855 3.498 5.346 6.876
beta_H[1,3] 8.531 0.245 8.100 8.514 9.045
beta_H[2,3] 10.127 0.111 9.907 10.127 10.343
beta_H[3,3] 9.663 0.158 9.359 9.661 9.988
beta_H[4,3] -1.869 0.932 -3.745 -1.869 -0.039
beta_H[5,3] 4.159 0.744 2.625 4.171 5.657
beta_H[6,3] 8.016 1.225 6.390 7.600 10.845
beta_H[7,3] -2.438 0.659 -3.731 -2.416 -1.194
beta_H[8,3] 7.669 2.532 4.833 6.342 11.853
beta_H[9,3] -1.933 0.694 -3.316 -1.920 -0.615
beta_H[10,3] 8.874 0.278 8.320 8.872 9.421
beta_H[11,3] 8.656 0.279 8.044 8.682 9.143
beta_H[12,3] 5.377 0.299 4.663 5.408 5.859
beta_H[13,3] 9.026 0.172 8.688 9.023 9.363
beta_H[14,3] 5.860 0.268 5.284 5.874 6.345
beta_H[15,3] 10.472 0.331 9.824 10.469 11.134
beta_H[16,3] 7.229 0.507 6.038 7.299 8.036
beta_H[1,4] 8.299 0.181 7.914 8.305 8.637
beta_H[2,4] 10.193 0.112 9.957 10.197 10.398
beta_H[3,4] 10.166 0.162 9.814 10.179 10.441
beta_H[4,4] 11.684 0.428 10.812 11.680 12.505
beta_H[5,4] 6.097 0.985 4.471 5.989 8.243
beta_H[6,4] 7.285 0.845 5.161 7.513 8.417
beta_H[7,4] 8.194 0.332 7.528 8.199 8.838
beta_H[8,4] 5.954 0.959 4.188 6.386 7.182
beta_H[9,4] 6.980 0.404 6.203 6.976 7.781
beta_H[10,4] 7.818 0.250 7.363 7.805 8.340
beta_H[11,4] 9.430 0.200 9.038 9.429 9.811
beta_H[12,4] 7.164 0.207 6.758 7.163 7.580
beta_H[13,4] 9.155 0.156 8.832 9.159 9.446
beta_H[14,4] 7.828 0.209 7.434 7.829 8.254
beta_H[15,4] 9.503 0.246 9.029 9.502 9.983
beta_H[16,4] 9.222 0.189 8.893 9.206 9.636
beta_H[1,5] 8.983 0.148 8.686 8.987 9.264
beta_H[2,5] 10.790 0.093 10.614 10.788 10.985
beta_H[3,5] 10.920 0.168 10.623 10.907 11.286
beta_H[4,5] 8.416 0.443 7.589 8.404 9.331
beta_H[5,5] 5.041 0.833 3.101 5.188 6.326
beta_H[6,5] 8.640 0.557 7.784 8.543 10.082
beta_H[7,5] 6.848 0.319 6.238 6.845 7.460
beta_H[8,5] 8.822 0.734 7.908 8.513 10.323
beta_H[9,5] 8.284 0.402 7.467 8.284 9.075
beta_H[10,5] 10.081 0.238 9.598 10.092 10.525
beta_H[11,5] 11.483 0.230 11.024 11.484 11.939
beta_H[12,5] 8.475 0.188 8.106 8.475 8.866
beta_H[13,5] 10.032 0.137 9.761 10.031 10.293
beta_H[14,5] 9.216 0.213 8.823 9.209 9.646
beta_H[15,5] 11.171 0.247 10.692 11.172 11.663
beta_H[16,5] 9.981 0.149 9.687 9.982 10.268
beta_H[1,6] 10.180 0.194 9.831 10.163 10.608
beta_H[2,6] 11.510 0.106 11.305 11.510 11.720
beta_H[3,6] 10.821 0.162 10.477 10.827 11.115
beta_H[4,6] 12.836 0.770 11.252 12.853 14.298
beta_H[5,6] 6.070 0.740 4.803 6.022 7.736
beta_H[6,6] 8.662 0.626 6.984 8.775 9.532
beta_H[7,6] 9.816 0.535 8.799 9.799 10.875
beta_H[8,6] 8.722 1.064 6.390 9.220 9.972
beta_H[9,6] 8.373 0.664 7.102 8.356 9.751
beta_H[10,6] 9.550 0.319 8.861 9.576 10.102
beta_H[11,6] 10.867 0.337 10.153 10.892 11.485
beta_H[12,6] 9.385 0.246 8.898 9.380 9.903
beta_H[13,6] 11.052 0.156 10.772 11.041 11.370
beta_H[14,6] 9.817 0.265 9.275 9.817 10.320
beta_H[15,6] 10.854 0.426 10.017 10.859 11.703
beta_H[16,6] 10.632 0.185 10.256 10.639 10.977
beta_H[1,7] 10.852 0.878 8.769 10.953 12.311
beta_H[2,7] 12.218 0.407 11.420 12.214 12.973
beta_H[3,7] 10.552 0.679 9.092 10.625 11.648
beta_H[4,7] 2.561 3.897 -4.950 2.462 10.529
beta_H[5,7] 7.080 2.678 2.416 6.744 13.260
beta_H[6,7] 9.430 2.256 5.054 9.291 15.606
beta_H[7,7] 10.842 2.727 5.301 10.956 15.956
beta_H[8,7] 14.222 4.686 9.221 11.733 25.152
beta_H[9,7] 4.716 3.492 -2.613 4.777 11.337
beta_H[10,7] 9.780 1.471 7.118 9.708 12.970
beta_H[11,7] 10.878 1.610 7.852 10.773 14.470
beta_H[12,7] 10.094 0.851 8.205 10.154 11.626
beta_H[13,7] 11.696 0.711 10.050 11.768 12.823
beta_H[14,7] 10.369 0.870 8.630 10.413 11.961
beta_H[15,7] 11.966 2.197 7.687 11.940 16.306
beta_H[16,7] 11.778 0.858 10.405 11.661 13.833
beta0_H[1] 8.626 14.165 -21.889 8.867 36.672
beta0_H[2] 10.706 5.825 -1.288 10.711 22.448
beta0_H[3] 9.852 9.343 -9.879 9.935 28.315
beta0_H[4] 5.712 174.917 -349.146 6.277 354.993
beta0_H[5] 4.528 40.249 -79.043 4.777 89.457
beta0_H[6] 7.564 43.662 -91.299 7.567 106.767
beta0_H[7] 3.557 128.891 -263.605 6.287 261.671
beta0_H[8] -1.550 258.277 -597.032 6.181 615.136
beta0_H[9] 10.484 108.096 -201.787 9.161 225.856
beta0_H[10] 8.024 33.697 -60.824 8.738 74.183
beta0_H[11] 9.762 42.399 -82.220 9.646 96.105
beta0_H[12] 6.373 9.681 -13.805 6.463 24.921
beta0_H[13] 9.670 9.858 -10.271 9.718 27.883
beta0_H[14] 6.898 10.688 -16.174 7.069 27.685
beta0_H[15] 8.525 102.605 -199.279 7.801 225.542
beta0_H[16] 8.339 14.691 -19.855 8.344 37.036